The order Caryophyllales, of which Japanese knotweed is a member, is a group of about 12,500 plant species distributed among 26 families. It's a diverse collection of flowering plants that includes succulents, cacti and carnivorous plants, as well as edible plants such as rhubarb, beets and spinach. One characteristic of Caryophyllales is that the plants form seeds that are attached either to the bottom of their fruit or to a central pillar inside the fruit.
The family to which Japanese knotweed belongs, Polygonaceae, is often referred to as the buckwheat family because the genus Erigonum, the buckwheats, is the largest in the family; the entire family encompasses about 1,100 species in 43 genera. The name of the family, which translates from Latin to something like "many knees," refers to swollen nodes along the plants' stems, a characteristic common to many plants in the family. The plants also usually produce an abundance of small flowers grouped in clusters or on flower spikes. Other notable plants in the family include rhubarb and sorrel.
The genus Polygonum is the collection of species that gave its name to the family Polygonaceae because the plants in this genus in particular have pronounced stem nodes. They also grow quickly and spread readily, which explains why the word "weed" shows up in the name of many species in the genus, including some species that are commonly referred to as smartweeds. The plants in this genus like moist soil, but they can handle dry soil if provided with shade. Similarly, they prefer full sun, but they can grow well, if less invasively, in part shade.
Japanese knotweed is one of the most problematic species in the genus. It produces large, hollow stems that can reach 6 to 10 feet in height; it's sometimes called Japanese bamboo because the tall, jointed stems resemble bamboo. These stems sprout from underground rhizomes that stretch as far as 30 feet from the parent plant. If the rhizomes are cut or otherwise broken up, new colonies are able to sprout from small sections of the rhizome that are inadvertently moved by gardeners or flowing water. Because it spreads so easily, controlling the weed is difficult, and it's classified as a noxious pest in many states.